Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding particles (as pseudo landmarks) on 3D surfaces to allow subsequent shape analysis. A recent deep learning approach leverages implicit radial basis function representations of shapes to better adapt to the underlying complex geometry of anatomies. Here, we propose an adaptation of this method using a traditional optimization approach that allows more precise control over the desired characteristics of models by leveraging both an eigenshape and a correspondence loss. Furthermore, the proposed approach avoids using a black-box model and allows more freedom for particles to navigate the underlying surfaces, yielding more informative statistical models. We demonstrate the efficacy of the proposed approach to state-of-the-art methods on two real datasets and justify our choice of losses empirically.